Even within this limited scope, we have restricted ourselves to “controlled” solutions - by which we mean either exact results (typically obtained using numerical methods of various sorts) or in cases where there is an approximation scheme that becomes asymptotically exact as an explicitly identified small parameter tends to zero. This has led us to omit discussion of a variety of new and powerful “mean-field” methods, including dynamical mean field theory and dynamical cluster approximations, which have profitably been applied to this problem. Fortunately, a companion paper to the present paper [1]} has these approaches as its complementary focus.
